Grade 10 Mathematics Rational Numbers.

Similar presentations

2 Curriculum Statement Algebraic ExpressionsUnderstand that real numbers can be rational or irrational.Establish between which two integers a simple surd lies.Round off to an appropriate degree of accuracy.Multiplication of a binomial by a trinomial.Factorisation – including: HCF, DOTS, trinomials, grouping, Sum and difference of 2 cubes.Simplification of algebraic fractions with denominators of cubes (limited to sum and difference of cubes)

3 Unit 1 Identify rational numbersA rational number (Q) is a fraction and can be either recurring or terminating.It may be a common fraction or a mixed number e.g orFractions can be written as a decimal fraction and vice versa e.g.andTerminating decimals are those that ends e.g. 0,5 or 1,25 or 0,678.A recurring decimal is a decimal fraction which repeats itself or part of it e.g. 0,33333……. orIrrational numbers do not terminate (end) or recur

5 Unit 1 Convert between terminating and common fractions.Examples:A terminating decimal is a ending decimal:

6 Unit 1 Converting between recurring decimals and common fractions.Convert 0,33… to a common fractionTo convert a recurring decimal into a common fraction:Multiply it by appropriate powersof 10Then use subtraction to eliminatethe repeating part.Then simplify the fraction.

7 Question Time 1) 2) 3) 4) Question 1 Which of the following numbersare rational :1)2)3)4)

9 Unit 1 Rounding Off Numbers to Certain Decimal PlacesThe rules for rounding off numbers to a certain number of decimal places are as follows:Count to the number of decimal places after the comma that youwant to round off to.Look at the digit to the right of that number:- if it is < 5, drop it and all the numbers to the right of it.- if it is ≥ 5, add one more digit to the previous digit, and then drop itand all the numbers to the right of it.- keep all zeros (place holders) where required

10 Question Time Question 1Round off the following to two decimal places:3,2562 Answer: 3,261, Answer: 1,892, Answer: 2,21

11 Unit 1 Representing Numbers on a Number LineSET BUILDER NOTATIONRead as: x is greater than or equal to four.Read as: x is greater than -5, and less than or equal to 3.INTERVAL NOTATION

12 Unit 1 Multiplication of Algebraic ExpressionsPRODUCT OF TWO BINOMIALSFirsts, Outers, Inners, Lasts (FOIL)SQUARING A BINOMIALSquare the firsts, Twice the product, Square the lastPRODUCT OF A BINOMIAL AND A TRINOMIALMultiply each term in the binomial by every term in the trinomial

15 Unit 1 Factorising Taking out a Highest Common Factor: (HCF)- Always do this first. Look for a numerical or variable factor that iscommon to each term in the polynomial.Difference of Two Squares: (DOTS) - When you see a “ ”Quadratic trinomial:- when you have a trinomial in the form ax² + bx + c

16 Unit 1 Factorising (cont.)4. Grouping- when you have 4 terms – group into two terms and then take out aHCF from each.- then take out a Highest common BracketSum and Difference of Two Cubes- when you have “ ” or “ ”- cube root each term to give you your fist bracket- then: square first, square last, product change the sign for your second bracket

17 Unit 1 Algebraic FractionsMultiplication and DivisionFactorise all parts of the expression. Cross cancel where applicable.

18 Unit 1 Algebraic FractionsAddition and Subtraction:Factorise all parts of the expression.Find a LCD and simplify

19 Unit 1 Simplify expressions using the laws of exponents.A product to n powers: a.a.a.a.a……….. is defined as :

21 Unit 1 Simplify expressions using the laws of exponents.A surd is the square root of a whole number which produces an irrational number.A surd is an irrational number ( you need a calculator to determine the numerical value of the surd e.g which is a never ending, non – recurring decimal.The surd lies between which can be writtenas:are surds, but we can simplify them further.Note:We may never root over a plus or minus sign e.g.

22 Unit 1 Simplify expressions using the laws of exponents.To use the ladder method to determine the factors of a number by using prime factors:Prime numbers: Numbers with only two factors i.e. 1 and itself: e.g. 3 = 3.1E.g. 2; 3; 5; 7; 11; 13; 17; 19; 23; 29; 31; 37 …We divide the smallest prime number into the number until we get 1:Worked Example:Use common factor here e.g.

27 Unit 1 Working with numbersf(x) is the function value or the y value.If f(-1) = 2, it means that when x = -1, then y = 2, and we then have the co-ordinate pair (-1;2).{(-2;3); (0;2); (3;2); (5;6)}Check to see if any of the x values are repeated. No ordered pair in the function has a first value that are repeated. It is a functionIf a graph is given, it is easier to run a vertical line, (use your ruler) from top to bottom and see if there is more than one point of intersection. If at all times we have only one point on the graph intersecting with our ruler, this is a function.Example:Given: {(1;2); (2;1); (2;2); (3;1); (3;2); (4;4)}…..Note: 2 and 3 are first components in two co-ordinate pairs!Domain: {1; 2; 3; 4}Range: {1; 2; 4} Not a function

28 Question Time Find: g(4) a if g(a) = 25 the domain of fA function is defined by g = {(3;2); (4;5); (8;25)}Find:g(4)a if g(a) = 25the domain of fthe range of f.